I am just wondering what Garry Kasparov has done that contributes to posterity for our society?

He made chess pretty well known. He probably contributed to the society of professional chess players making more money. He constantly promotes chess which is not a bad thing to promote.

He did those historical, Deep Blue games. It proved there are loop holes in the Laws of Robotics.

How does that make society prosper, MyCows?

OP said "Posterity" in the title. I think that has something to do with rear ends. Now that I re-read it, he asks about prosperity for posterity. Since I didn't understand it, I answered a different question. However, the Deep Blue games did promote chess for a bit. Perhaps, that promoted prosperity for posterity.

Hilarious! That would be posterior. His job was sitting down for hours, so it probably didn't help his posterior.

Actually Nizman wants Kasparov to put his posterior on the chess board?! I don't know if that would help?